Hi ! , first of all we have to find the common denominator, which is basically a number that 9 and 8 have in common , in this case the common denominator is 72 . I personally prefer to change the mixed fractions , so if you don't change them it's fine , but it is easier if you do. We multiply 8 by 5 which is 40 them were add one to 40 , so our improper fraction is 41/1 , we do the same thing to the other one . Now that we have the improper fractions and the common denominator, we multiply the whole fraction by the number that times the denominator gives us 72.
5 1/8= 41/8
8 7/9= 79/9
41/8 times 9 = 369/72
79/9 times 8= 632/72
After that we add the fractions , 369/72+632/72
Our final answer is 1001/72